A fermion dark matter candidate with a relic abundance set by annihilation through a pseudoscalar can evade constraints from direct detection experiments. We present simplified models that realize this fact by coupling a fermion dark sector to a two-Higgs doublet model. These models are generalizations of mixed bino-Higgsino dark matter in the MSSM, with more freedom in the couplings and scalar spectra. Annihilation near a pseudoscalar resonance allows a significant amount of parameter space for thermal relic dark matter compared to singlet-doublet dark matter, in which the fermions couple only to the SM Higgs doublet. In a general two-Higgs doublet model, there is also freedom for the pseudoscalar to be relatively light and it is possible to obtain thermal relic dark matter candidates even below 100 GeV. In particular, we find ample room to obtain dark matter with mass around 50 GeV and fitting the Galactic Center excess in gamma-rays. This region of parameter space can be probed by LHC searches for heavy pseudoscalars or electroweakinos, and possibly by other new collider signals.

v2: added references, fermi dwarf constraints added to figures